Saturday, 12 May 2012

A Theory Into Why It Should Be Cheaper Driving North

This post has nothing to do with IT,
just happened to have been a curiosity conjured during my travels up North and
back down South on various IT projects.

Hypothesis

The Earth is not a perfect sphere, it
is a spheroid that bulges out at the equator – the Earth's
equatorial radius is greater than the Earth's polar radius. From
high-school physics we know that Potential
Energy = mass
x gravity
x heightand so it follows that we might expect the potential
energy of an object on the Earth's surface (sea-level) at the
equator, to be greater than the potential energy of an object on the
Earth's surface closer to the poles, since we can think of sea-level
at the equator as being higher (further away from the Earth's
core/center of mass) than sea-level close to the poles.

Application of the Hypothesis

If I travel from London to Glasgow
achieving an MPG of 50 (Diesel),
by how much would I expect the MPG to be affected on the drive back
from Glasgow to London (because of the need to burn more fuel to
acquire the additional potential energy)?

This application is based on a complete
fantasy scenario where there are no traffic problems, the road is
upon a perfectly flat spheroidal Earth (it could be argued that even
with undulations in the carriageway, would still need to acquire more
potential energy on the drive to London,) and I travel from sea-level
in London to sea-level in Glasgow, and is really more of a
mathematical exercise that attempts to calculate if there would be
any noticeable difference. Apologies in advance for any flaws in the calculations!

The Mathematics

An old copy of Maple 7 was used for
the calculations, and some of the lines below in red represent the Maple
Execution Group Inputs with some formulas in blue.